For loop and computational time

My code is taking much longer to run. Is there any way I can make it faster.

Here is my code.

clear td to w d m phi wp dk Ham Hu Idd Gh huu e2 x t T H
clear p q h qmax alpha A1 q1 Q aalpha g hd Hf L aaa k1 k2 k td tdd j ja i j1 a H T v all_v e e1
tic
td = 1;
phi = (2*pi)/3;
w = 110;
qmax = 120;
for i = 1:1:qmax
    if i>2
       q(i)=i;
       for j = 1:1:i
           p(j) = j-1;
           A1(i,j)=sym(p(j)/q(i));
       end
    end
end
alpha = unique(reshape(A1',1,[]));
[p,q1] = numden(sym(alpha));
for i = 1:1:length(alpha)
    if double(q1(i))>2
       Q(i) = double(q1(i));
       aalpha(i) = double(alpha(i));
    else Q(i) = 3;
         aalpha(i)= 1/3;
    end
end
figure1 = figure;
axes1 = axes('Parent',figure1)
hold(axes1,'all');
for i= 1:1:length(aalpha)
     H = zeros(2*Q(i),2*Q(i));
     L1 = 4*pi*aalpha(i);
     L2 = 2*pi/(double(Q(i)));
     k1 = 0:L1/10:L1;
     k2 = 0:L2/10:L2;
    for l1 = 1:1:length(k1)
        for h2 = 1:1:length(k2)
            for j = 1:2:2*Q(i)-1
                H(j,j+1)=w*td*exp(-2*pi*(aalpha(i)/sqrt(3))-1i*(1*k1(l1)+4*pi*aalpha(i)*(j-1)/2));
                H(j+1,j)=conj(w*td*exp(-2*pi*(aalpha(i)/sqrt(3))-1i*(1*k1(l1)+4*pi*aalpha(i)*(j-1)/2)));
            end
            for j = 2:2:2*Q(i)-2
                H(j+1,j)=conj(w*td*exp(1i*phi)*exp(-2*pi*(aalpha(i)/sqrt(3))+1i*(1*k1(l1)/2+1*pi*aalpha(i)*((2*(j-2)/2)+1))-1i*1*k2(h2)));
                H(j,j+1)=w*td*exp(1i*phi)*exp(-2*pi*(aalpha(i)/sqrt(3))+1i*(1*k1(l1)/2+1*pi*aalpha(i)*((2*(j-2)/2)+1))-1i*1*k2(h2));
            end
            for j = 1:2:2*Q(i)-3
                H(j,j+3)=w*td*exp(-1i*phi)*exp(-2*pi*(aalpha(i)/sqrt(3))+1i*(1*k1(l1)/2+1*pi*aalpha(i)*(2*((j-1)/2)-1))+1i*1*k2(h2));
                H(j+3,j)=conj(w*td*exp(-1i*phi)*exp(-2*pi*(aalpha(i)/sqrt(3))+1i*(1*k1(l1)/2+1*pi*aalpha(i)*(2*((j-1)/2)-1))+1i*1*k2(h2)));
            end
            H(1,2*double(Q(i))) =1* w*td*exp(-1i*phi)*exp(-2*pi*(aalpha(i)/sqrt(3))+1i*(1*(k1(l1)/2)+1*pi*aalpha(i)*(2*double(Q(i))-1))+1i*1*k2(h2));
            H(2*double(Q(i)),1) = conj(1* w*td*exp(-1i*phi)*exp(-2*pi*(aalpha(i)/sqrt(3))+1i*(1*(k1(l1)/2)+1*pi*aalpha(i)*(2*double(Q(i))-1))+1i*1*k2(h2)));
            H(2*double(Q(i))-1,2) =1*conj(w*td*exp(1i*phi)*exp(-2*pi*(aalpha(i)/sqrt(3))+1i*(1*(k1(l1)/2)+1*pi*aalpha(i)*(2*(double(Q(i)))+1))-1i*1*k2(h2)));
            H(2,2*double(Q(i))-1) = 1*w*td*exp(1i*phi)*exp(-2*pi*(aalpha(i)/sqrt(3))+1i*(1*(k1(l1)/2)+1*pi*aalpha(i)*(2*(double(Q(i)))+1))-1i*1*k2(h2));
            e2= eig(H);
            hold on
            plot(aalpha(i),e2,'.','MarkerSize',1);
        end
    end
end
hold off
%saveas(figure1,'Perfect.pdf')
timeelapsed = toc 

[Rik]

The first step would probably be to use the profiler to determine the bottlenecks. Did you do that?

[per isakson]

See profile, Profile execution time for functions

Replacing parfor by for seems to save a lot of time ( on my system ).

Answer 1

[Raymond Norris]

Hi Muhammad,

I would suggest provide a bit more information when it comes to performance questions

• Which version of MATLAB?
• How many cores?
• How much memory?
• How long does it take to run your code?
• How long would you like it to take?

For me, your code appears to take less then 2s to run on 4 cores. Might be tough to eack out a lot more. A couple of suggestions

• The MATLAB Code Analyzer highlights a few suggestions (e.g. preallocation). I would suggest going through each of the recommendations.
• You might see slightly better performance writing this as a function (even without input/outputs) then a script
• As it's written, you can't plot figures within a parfor -- keep in mind, the body of the code is being executed on a separate worker(s) that are not sharing the MATLAB clients figure window. If you want to plot with a parfor, look at setting up a parallel.pool.DataQueue. In fact, one of the examples in the doc for it shows updating a waitbar.

Raymond

[muhammad imran]

@Raymond: This is because by mistake I have put qmax equal to 3. But for real run it will be qmax = 120. This means the dimension of the matrix go upto 120 times 120. I have I-7 processor with 6 cores, and 16 GB RAM.